NEURAL NETWORK BASED SOFTWARE PACKAGE FOR OPERATIONS RESEARCH PROBLEMS

Abstract

The objective of the present work is to get an idea of how to use Neural Networks in solving Operation Research problems. Attempts were made to solve Linear programming problem and the Traveling Sales Person problem using the Neural Networks. Success has been achieved in solving the Traveling Sales Person problem and it has been solved for up to a seven city problem using the Hopfield Network. It is presented as an example of nonlinear optimization with Neural Networks in this Thesis. Details of formulation of the energy function and it's evaluation are given. The solution obtained is good if not optimal. The problem with the Hopfield approach lies in the selection\ of the appropriate values of the various parameters appearing in the energy function. These were selected by trial and error procedure and gave satisfactory results for the Traveling Sales/ Person problem involving seven or fewer cities. The Traveling Sales Person problem was also solved using the conventional method and the program execution time for the conventional method of solution was compared with that of the developed software which used Neural Networks. The Traveling Sales Person problem belongs to a set of NP- complete problems. The NP-complete problems have the distinction that there is no known algorithm that is efficient and practical and there is little likelihood that such an algorithm will be developed in the future. This was the caveat kept in mind when we used the Neural Networks to solve the